The paper concerns the Gelfand-Kirillov dimension and the generating series
of nonsymmetric operads. An analogue of Bergman's gap theorem is proved,
namely, no finitely generated locally finite nonsymmetric operad has
Gelfand-Kirillov dimension strictly between 1 and 2. For every rβ{0}βͺ{1}βͺ[2,β) or r=β, we construct a single-element
generated nonsymmetric operad with Gelfand-Kirillov dimension r. We also
provide counterexamples to two expectations of Khoroshkin and Piontkovski about
the generating series of operads.Comment: 32 pages, 9 figure